The present invention relates to a new and distinct variety of peach tree named ‘NJ358’. Our new tree resulted from crossing ‘Flameprince’ (non-patented) as the seed parent with our proprietary peach seedling selection ‘G47-99-84258’ (non-patented) as the pollen parent. The new variety differs from seed parent ‘Flameprince’ in that the new variety produces larger fruit and that have better flavor and aromatics. The new variety differs from pollen parent ‘G47-99-84258’ in that the new variety has more tolerance to bacterial leaf spot and produces larger fruit that have a more uniform round shape. The resulting tree was selected when growing in a cultivated area as the 197th tree in the 64th row of Block K at a fruit research farm in Cream Ridge, N.J.